Mathematics

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14 pages, 431 KiB

Open AccessArticle

Robust Transceiver Design for Correlated MIMO Interference Channels in the Presence of CSI Errors under General Power Constraints

by Jae-Mo Kang and Dong-Woo Lim

Mathematics 2024, 12(6), 801; https://doi.org/10.3390/math12060801 - 08 Mar 2024

Viewed by 405

Abstract

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the [...] Read more.

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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19 pages, 435 KiB

Open AccessArticle

The k-out-of-n:G System Viewed as a Multi-Server Queue

by Achyutha Krishnamoorthy, Anu Nuthan Joshua and Ambily P. Mathew

Mathematics 2024, 12(2), 210; https://doi.org/10.3390/math12020210 - 08 Jan 2024

Cited by 1 | Viewed by 422

Abstract

This paper extends the k-out-of-n:G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N-policy of repair. The queuing system considered here has n servers, each of which has identically and exponentially distributed [...] Read more.

This paper extends the k-out-of-n:G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N-policy of repair. The queuing system considered here has n servers, each of which has identically and exponentially distributed service times with parameter

μ

. Servers are subject to breakdown at an exponential rate

γ

. The repair process follows the N-policy of repair. Although these servers work independently of each other, service can be provided only when k functional servers are available in the system. We study the model in the steady state, using the matrix analytic method. We evaluate some associated performance measures and provide graphical/numerical illustrations. We consider an optimization problem, and the results of the study are presented. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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25 pages, 316 KiB

Open AccessArticle

A Two-Server Queue with Interdependence between Arrival and Service Processes

by Sindhu S, Achyutha Krishnamoorthy and Dmitry Kozyrev

Mathematics 2023, 11(22), 4692; https://doi.org/10.3390/math11224692 - 18 Nov 2023

Viewed by 1876

Abstract

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and [...] Read more.

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

18 pages, 329 KiB

Open AccessArticle

On Positive Recurrence of the M_n/GI/1/∞ Model

by Alexander Veretennikov

Mathematics 2023, 11(21), 4514; https://doi.org/10.3390/math11214514 - 01 Nov 2023

Viewed by 536

Abstract

Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence [...] Read more.

Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

14 pages, 301 KiB

Open AccessArticle

Gibbs Distribution and the Repairman Problem

by Hassan Chetouani and Nikolaos Limnios

Mathematics 2023, 11(19), 4120; https://doi.org/10.3390/math11194120 - 29 Sep 2023

Viewed by 572

Abstract

In this paper, we obtain weak convergence results for a family of Gibbs measures depending on the parameter

θ > 0

in the following form [...] Read more.

In this paper, we obtain weak convergence results for a family of Gibbs measures depending on the parameter

θ > 0

in the following form

d P_{θ} (x) = Z_{θ} exp (- H_{θ} (x) / θ) d Q (x)

, where we show that the limit distribution is concentrated in the set of the global minima of the limit Gibbs potential. We also give an explicit calculus for the limit distribution. Here, we use the above as an alternative to Lyapunov’s function or to direct methods for stationary probability convergence and apply it to the repairman problem. Finally, we illustrate this method with a numerical example. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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27 pages, 2486 KiB

Open AccessArticle

Redundancy Allocation of Components with Time-Dependent Failure Rates

by Enrico Zio and Hadi Gholinezhad

Mathematics 2023, 11(16), 3534; https://doi.org/10.3390/math11163534 - 16 Aug 2023

Cited by 1 | Viewed by 768

Abstract

The Redundancy Allocation Problem (RAP) is well-known in the field of reliability optimization. In this paper, RAP is investigated assuming that the distribution of the time to failure of the components has the form of an Erlang distribution with a time-dependent rate parameter [...] Read more.

The Redundancy Allocation Problem (RAP) is well-known in the field of reliability optimization. In this paper, RAP is investigated assuming that the distribution of the time to failure of the components has the form of an Erlang distribution with a time-dependent rate parameter and considering that the choice of redundancy for each subsystem can be none, active, standby or mixed. A genetic algorithm is used to solve the problem of optimal allocation. To analyze the effect of the time dependence, some numerical examples are worked out. Then, a case study of RAP from the literature is analyzed. The obtained results show that time dependence of the failure time distribution parameters can lead to significant differences in the optimal redundancy allocation. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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27 pages, 919 KiB

Open AccessArticle

Event-Triggered Extended Dissipativity Fuzzy Filter Design for Nonlinear Markovian Switching Systems against Deception Attacks

by Mourad Kchaou and Mohamed Amin Regaieg

Mathematics 2023, 11(9), 2064; https://doi.org/10.3390/math11092064 - 26 Apr 2023

Cited by 2 | Viewed by 1063

Abstract

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an [...] Read more.

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an improved event-triggering mechanism to reduce the unnecessary signal transmissions on the communication channel and formulate the extended dissipativity specification to quantify the transient dynamics of filtering errors. By resorting to the linear matrix inequality approach and using the information on upper and lower membership functions, stochastic analysis establishes sufficient conditions for the existence of the desired filter, ensuring the mean-squared stability and extended dissipativity of the augmented filtering system. Further, an optimization-based algorithm (PSO) is proposed for computing filter gains at an optimal level of performance. The developed scheme was finally tested through experimental numerical illustrations based on a single-link robot arm and a lower limbs system. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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10 pages, 295 KiB

Open AccessArticle

Asymptotic Relations in Applied Models of Inhomogeneous Poisson Point Flows

by Gurami Tsitsiashvili and Marina Osipova

Mathematics 2023, 11(8), 1881; https://doi.org/10.3390/math11081881 - 15 Apr 2023

Cited by 1 | Viewed by 961

Abstract

A model of a particle flow forming a copy of some image and the distance between the copy and the image are estimated using a special probability metric. The ability of the flow of balls to cover the surface, when grinding the balls, [...] Read more.

A model of a particle flow forming a copy of some image and the distance between the copy and the image are estimated using a special probability metric. The ability of the flow of balls to cover the surface, when grinding the balls, was investigated using formulas of stochastic geometry. Reconstruction of characteristics of an inhomogeneous Poisson flow by inaccurate observations is analysed using the Poisson flow point colouring theorem. The dependence of the Poisson parameter of the distribution of the number of customers in a queuing system with an infinite number of servers and a deterministic service time on the peak load created by an inhomogeneous input Poisson flow is estimated. All these models consist of an inhomogeneous Poisson flow of points and marks glued to each point of the flow and are characterised by their mass, area, volume, observability (or non-observability), and service time. The presence of an asymptotic power–law relationship between model objective functions and parameters of mark crushing is established. These results may be applied in nanotechnology, powder metallurgy, ecology, and consumer services in the implementation of the “Smart City” program. The proposed approach is phenomenological in nature and is justified by the results of real observations and experiments. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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10 pages, 266 KiB

Open AccessArticle

Large Deviations for Hawkes Processes with Randomized Baseline Intensity

by Youngsoo Seol

Mathematics 2023, 11(8), 1826; https://doi.org/10.3390/math11081826 - 12 Apr 2023

Viewed by 700

Abstract

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with a clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of self-exciting point processes, [...] Read more.

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with a clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of self-exciting point processes, the Hawkes model is generally not Markovian. In certain special circumstances, it can be Markovian with a generator of the model if the exciting function is an exponential function or the sum of exponential functions. In the case of non-Markovian processes, difficulties arise when the exciting function is not an exponential function or a sum of exponential functions. The intensity of the Hawkes process is given by the sum of a baseline intensity and other terms that depend on the entire history of the point process, as compared to a standard Poisson process. It is one of the main methods used for studying the dynamical properties of general point processes, and is highly important for credit risk studies. The baseline intensity, which is instrumental in the Hawkes model, is usually defined for deterministic cases. In this paper, we consider a linear Hawkes model where the baseline intensity is randomly defined, and investigate the asymptotic results of the large deviations principle for the newly defined model. The Hawkes processes with randomized baseline intensity, dealt with in this paper, have wide applications in insurance, finance, queue theory, and statistics. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

26 pages, 625 KiB

Open AccessArticle

A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input

by Mohan Chaudhry, Abhijit Datta Banik, Sitaram Barik and Veena Goswami

Mathematics 2023, 11(5), 1142; https://doi.org/10.3390/math11051142 - 24 Feb 2023

Cited by 4 | Viewed by 1345

Abstract

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following a Poisson process and the server operates under

(a, b)

-bulk service rule. The queueing system has a finite-buffer capacity [...] Read more.

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following a Poisson process and the server operates under

(a, b)

-bulk service rule. The queueing system has a finite-buffer capacity ‘N’ excluding the batch in service. The service-time distribution of batches follows a general distribution, which is independent of the arrival process. We first develop an alternative approach of obtaining the probability distribution for the queue length at a post-departure epoch of a batch and, subsequently, the probability distribution for the queue length at a random epoch using an embedded Markov chain, Markov renewal theory and the semi-Markov process. The waiting-time distribution (in the queue) of a random customer is derived using the functional relation between the probability generating function (pgf) for the queue-length distribution and the Laplace–Stieltjes transform (LST) of the queueing-time distribution for a random customer. Using LSTs, we discuss the derivation of the probability density function of a random customer’s waiting time and its numerical implementations. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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22 pages, 3682 KiB

Open AccessArticle

An Adoptive Miner-Misuse Based Online Anomaly Detection Approach in the Power System: An Optimum Reinforcement Learning Method

by Abdulaziz Almalaq, Saleh Albadran and Mohamed A. Mohamed

Mathematics 2023, 11(4), 884; https://doi.org/10.3390/math11040884 - 09 Feb 2023

Cited by 2 | Viewed by 1183

Abstract

Over the past few years, the Bitcoin-based financial trading system (BFTS) has created new challenges for the power system due to the high-risk consumption of mining devices. Briefly, such a problem would be a compelling incentive for cyber-attackers who intend to inflict significant [...] Read more.

Over the past few years, the Bitcoin-based financial trading system (BFTS) has created new challenges for the power system due to the high-risk consumption of mining devices. Briefly, such a problem would be a compelling incentive for cyber-attackers who intend to inflict significant infections on a power system. Simply put, an effort to phony up the consumption data of mining devices results in the furtherance of messing up the optimal energy management within the power system. Hence, this paper introduces a new cyber-attack named miner-misuse for power systems equipped by transaction tech. To overwhelm this dispute, this article also addresses an online coefficient anomaly detection approach with reliance on the reinforcement learning (RL) concept for the power system. On account of not being sufficiently aware of the system, we fulfilled the Observable Markov Decision Process (OMDP) idea in the RL mechanism in order to barricade the miner attack. The proposed method would be enhanced in an optimal and punctual way if the setting parameters were properly established in the learning procedure. So to speak, a hybrid mechanism of the optimization approach and learning structure will not only guarantee catching in the best and most far-sighted solution but also become the high converging time. To this end, this paper proposes an Intelligent Priority Selection (IPS) algorithm merging with the suggested RL method to become more punctual and optimum in the way of detecting miner attacks. Additionally, to conjure up the proposed detection approach’s effectiveness, mathematical modeling of the energy consumption of the mining devices based on the hashing rate within BFTS is provided. The uncertain fluctuation related to the needed energy of miners makes energy management unpredictable and needs to be dealt with. Hence, the unscented transformation (UT) method can obtain a high chance of precisely modeling the uncertain parameters within the system. All in all, the F-score value and successful probability of attack inferred from results revealed that the proposed anomaly detection method has the ability to identify the miner attacks as real-time-short as possible compared to other approaches. Full article

(This article belongs to the Special Issue Probability and Stochastic Processes with Applications to Communications, Systems and Networks, 2nd Edition)

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